Primordial hypermagnetic fields and the triangle anomaly

The high-temperature plasma above the electroweak scale $\sim 100\mathrm{GeV}$ may have contained a primordial hypercharge magnetic field whose anomalous coupling to the fermions induces a transformation of the hypermagnetic energy density into fermionic number. In order to describe this process, we generalize the ordinary magnetohydrodynamical equations to the anomalous case. We show that a not completely homogeneous hypermagnetic background induces fermion-number fluctuations, which can be expressed in terms of a generic hypermagnetic field configuration. We argue that, depending upon the various particle physics parameters involved in our estimate (electron Yukawa coupling, strength of the electroweak phase transition) and upon the hypermagnetic energy spectrum, sizable matter-antimatter fluctuations can be generated in the plasma. These fluctuations may modify the predictions of the standard big bang nucleosynthesis (BBN). We derive constraints on the magnetic fields from the requirement that the homogeneous BBN is not changed. We analyze the influence of primordial magnetic fields on the electroweak phase transition and show that some specific configurations of the magnetic field may be converted into net baryon number at the electroweak scale.